Lensing and imaging by a stealth defect of spacetime

Abstract

We obtain the geodesics for the simplest possible stealth defect which has a flat spacetime. We, then, discuss the lensing properties of such a defect, and the corresponding image formation. Similar lensing properties can be expected to hold for curved-spacetime stealth defects.

Geodesic congruences in modified Schwarzschild black holes

“…We emphasize that the corresponding spacetime is geodesic complete, particles can safely cross the defect surface (see Ref. [21] for a detailed discussion. )…”

On a soliton-type spacetime defect

“…Consider the behavior of light rays propagating over a spacetime-defect manifold. It is, in fact, possible to give a simplified discussion [9] by use of an exact vacuum solution [10],…”

“…6 in Ref. [9] for further details). In principle, we can also obtain an exact multi-defect solution of the vacuum Einstein equation which is approximately Lorentz invariant, if we superpose quasi-randomly positioned and quasi-randomly moving l = 0 defects (arranged to be nonintersecting initially).…”

“…The aim of the present contribution is to provide a more or less self-contained discussion of one particular soliton-type classical solution, namely a Skyrmion spacetime defect solution [6] and to explain the origin of certain new phenomena [7,8,9]. In Sec.…”

Non-metric construction of spacetime defects

“…The modification of the geodesic when crossing the defect (the region S R ) depends entirely on the specific choice of Ω. In an exact description of a spacetime defect (represented by nontrivial topology in the region S R ), this modification is entirely determined by the boundary conditions of the surface of S R (see for example [17]). On the one hand, it is not very difficult to convince oneself that, within this point of view, a judicious choice of Ω would allow to mimic the effects of the nontrivial topology.…”